We consider complex-valued solutions uε of the Ginzburg-Landau equation on a smooth bounded simply connected domain Ω of ℝN, N≥2, where ε>0 is a small parameter. We assume that the Ginzburg-Landau energy Eε(uε) verifies the bound (natural in the context) Eε(uε)≤M0|logε|, where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of uε, as ε→0, is to establish uniform Lp bounds for the gradient, for some p>1. We review some recent techniques developed in the elliptic case in [7], discuss some variants, and extend the methods to the associated parabolic equation.